The enormous size of the diagonal Latin squares space makes it unfeasible to enumerate all its objects straightforwardly in reasonable time. So, in order to discover the structure of this space, sophisticated search methods are needed. In RakeSearch project, we implement an application that picks up separate pairs of mutually orthogonal DLSs, which allows to reconstruct full graphs of their orthogonality. You can contribute to our research by running a free program on your computer.
For account creation please use a Crunch_4Science invitation code.
Joint search of ODLS9 with Gerasim project
A new search started in the project on September 27 - "Joint search of ODLS9 with Gerasim project". Earlier we performed a full search over the space of row-permutational diagonal Latin squares of order 9, but in this search (that we perform with Gerasim@Home project) we try to find all orthogonal diagonal Latin squares of order 9! At the first glance, the goal is unreachable, but the new search uses an heuristics that allowed to reduce the amount of computations.
In this thread we will post news about the new search.
15 Oct 2020, 18:01:30 UTC · Discuss
Results of SAT-CMS
As a result of the SAT-CMS experiment, 29 pairs of orthogonal diagonal Latin squares (ODLS) of order 10 were found. 2 cell mapping schemas (CMS) were used for this purpose. 18 found pairs are based on the first CMS, the remaining 11 pairs are based on the second one. CMS is in fact a relation between 2 Latin square from an orthogonal pair: for each element of the first square it shows where this element should be placed in the second square. Therefore, one can effectively construct the second square from a pair given the first square. The computing application was based on the CDCL algorithm aimed at solving the Boolean satisfiability problem (SAT). For each studied CMS, we first reduced a problem of finding pairs of ODLS of order 10 (that match the CMS) to SAT. Then, the obtained SAT problem was splitted into subproblems which in turn formed workunits. Finally, from found satisfying assignments (solutions of the SAT problems) we constructed the corresponding pairs of ODLS. All the found pairs are listed here. We are very grateful to all the crunchers who took part in the experiment!
27 Sep 2020, 17:30:31 UTC · Discuss
Some news about next search
Dear participants, we try to start distribution of tasks to new search. Errors during start and computing are possible. :)
27 Sep 2020, 12:15:12 UTC · Discuss
SAT-CMS-based search badge!
Most workunits of the SAT-CMS-based search of orthogonal diagonal Latin squares (ODLS) of order 10 has been completed, so we grant a new badge to participants whose computers found solutions in it. Each solution contains at least one pair of ODLS. Since Dr. Oleg Zaikin, the leading scientist of this study, works in Irkutsk, Siberia, he chose a wonderful Siberian animal Cabarga (or Siberian musk deer) to be depicted in the badge. After post-processing of results we are planning to publish full results of this search. However, the badge is given right now, and we send our warm congratulations to:
[AF>Libristes] Davlabedave (L'Alliance Francophone) and KySU,
Megacruncher TSBT (The Scottish Boinc Team) and applish,
scole of TSBT (The Scottish Boinc Team) and Rene Schimmer,
Cruncher Pete (The Scottish Boinc Team) and Bok (SETI.USA),
davidBAM (The Scottish Boinc Team) and yiqiL (Team China),
Konstantin Desyatkin (Russia Team) and Ufol (BOINC@Poland),
Rhodan71 (L'Alliance Francophone) and MaZZaY (Russia Team),
Ron Shurtz [BlackOps] (SETI.USA) and Odd-Rod (BOINCstats),
EarlyBird@Zircons (BOINC@Taiwan) and alexey (Russia Team),
KAMCOBILL (X Grubbers Kick Ass) and RFGuy_KCCO ([H]ardOCP),
=Lupus= (BOINC Confederation) and JagDoc (Planet 3DNow!),
boceli (Czech National Team) and CFJH (Rechenkraft.net),
DoctorNow (BOINC@Heidelberg) and Spritex (BOINC@Denmark),
Fardringle (TeAm AnandTech) and ssjy806 (SETIKAH@KOREA),
[B@P] Daniel (BOINC@Poland) and Woodles (UK BOINC Team),
ReaDy (Astronomy.Ru Forum) and zombie67 [MM] (SETI.USA),
Lycidas (BOINC@Heidelberg) and CoolAtchOk (Russia Team),
Sengieffe (UK BOINC Team) and Diffident (Overclock.net).
Only 36 participants received this badge!
Thank you for your attention to the project and donation of CPU time!
3 Sep 2020, 18:50:35 UTC · Discuss
First workunits of new search will be generated soon
In next few hours the first, small and test bunch of new workunits will be generated. Later we will tell more about this experiment.
Thank you for attention and participation!
The RakeSearch project team.
20 Jul 2020, 6:56:25 UTC · Discuss
©2020 The searchers team, Karelian Research Center of the Russian Academy of Sciences